Rewrite (x+2)(x-4) in Standard Quadratic Form

Q: What does FOIL stand for and why do I need it?

FOIL stands for First, Outer, Inner, Last - the order you multiply terms in two binomials. It ensures you don't miss any terms when expanding $ (x+2)(x-4) $!

Q: How do I know which terms are 'like terms'?

Like terms have the same variable and power. In $ x^2 - 4x + 2x - 8 $, the terms $ -4x $ and $ +2x $ are like terms because they both have x to the first power.

Q: What if I get the signs wrong when FOILing?

Be extra careful with negative signs! In $ (x+2)(x-4) $, the Outer term is $ x \times (-4) = -4x $ and Last term is $ 2 \times (-4) = -8 $. Watch those minus signs!

Q: What is 'standard form' for a quadratic?

Standard form is $ ax^2 + bx + c $ where terms are arranged in descending order of powers. So $ x^2 - 2x - 8 $ is in standard form!

Quadratic Expansion with FOIL Method

Find the standard representation of the following function

$f(x)=(x+2)(x-4)$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simplify to the standard representation of the function

00:04 Open parentheses properly, multiply each factor by each factor

00:15 Collect terms

00:24 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the standard representation of the following function

$f(x)=(x+2)(x-4)$

Step-by-step solution

To find the standard representation of the quadratic function given by $f(x) = (x+2)(x-4)$ , we will expand the expression using the distributive property, commonly known as the FOIL method (First, Outer, Inner, Last):

First: Multiply the first terms in each binomial: $x \cdot x = x^2$ .
Outer: Multiply the outer terms in the binomials: $x \cdot (-4) = -4x$ .
Inner: Multiply the inner terms: $2 \cdot x = 2x$ .
Last: Multiply the last terms in each binomial: $2 \cdot (-4) = -8$ .

Now, let's combine these results:

The expression becomes $x^2 - 4x + 2x - 8$ .

Next, we combine like terms:

The terms involving $x$ are $-4x + 2x$ , which simplifies to $-2x$ .

Thus, the expression simplifies to: $f(x) = x^2 - 2x - 8$

Upon comparing this result to the provided choices, we find that it matches choice 3.

Therefore, the standard representation of the function is $f(x) = x^2 - 2x - 8$ .

Final Answer

$f(x)=x^2-2x-8$

Key Points to Remember

Essential concepts to master this topic

FOIL Method: First, Outer, Inner, Last to multiply binomials
Technique: $(x+2)(x-4) = x^2 - 4x + 2x - 8$
Check: Combine like terms: $-4x + 2x = -2x$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms after FOIL
Don't leave your answer as $x^2 - 4x + 2x - 8$ = incomplete expansion! This doesn't show standard form and looks messy. Always combine like terms: $-4x + 2x = -2x$ to get $x^2 - 2x - 8$ .

Practice Quiz

Test your knowledge with interactive questions

Create an algebraic expression based on the following parameters:

$$ a=2,b=2,c=2 $$

FAQ

Everything you need to know about this question

What does FOIL stand for and why do I need it?

FOIL stands for First, Outer, Inner, Last - the order you multiply terms in two binomials. It ensures you don't miss any terms when expanding $(x+2)(x-4)$ !

How do I know which terms are 'like terms'?

Like terms have the same variable and power. In $x^2 - 4x + 2x - 8$ , the terms $-4x$ and $+2x$ are like terms because they both have x to the first power.

What if I get the signs wrong when FOILing?

Be extra careful with negative signs! In $(x+2)(x-4)$ , the Outer term is $x \times (-4) = -4x$ and Last term is $2 \times (-4) = -8$ . Watch those minus signs!

Is there a way to check my final answer?

Yes! Pick any value for x and substitute into both the original $(x+2)(x-4)$ and your answer $x^2-2x-8$ . If you get the same result, you're correct!

What is 'standard form' for a quadratic?

Standard form is $ax^2 + bx + c$ where terms are arranged in descending order of powers. So $x^2 - 2x - 8$ is in standard form!

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Rewrite (x+2)(x-4) in Standard Quadratic Form

Quadratic Expansion with FOIL Method

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

What does FOIL stand for and why do I need it?

How do I know which terms are 'like terms'?

What if I get the signs wrong when FOILing?

Is there a way to check my final answer?

What is 'standard form' for a quadratic?

🌟 Unlock Your Math Potential

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